I. Field of the Invention
The present invention generally relates to providing systems and methods of guidance of an object and, in particular, to improvements in homing guidance. The present invention constitutes an improvement over prior known guidance laws. More particularly, the present invention relates to providing systems and method that use improved guidance laws that are an improvement over the proportional navigation guidance laws (PRONAV).
II. Background Information
Various methods and systems of missile guidance and missile homing guidance are known prior to the present invention. The approach that has come to dominate missile guidance research and development is known as Proportional Navigation (PN). PN was developed by C. Yuan at RCA Laboratories during World War II based on physical intuition. This guidance law states that a commanded acceleration is proportional to a line of sight (LOS) rate. A proportionality constant, associating the commanded acceleration and the LOS rate, can be broken down into the product of an effective navigation ratio times a relative missile-target closing velocity.
Two decades later, a quasi-optimality of PN was derived. The prefix “quasi” means that PN was obtained as a linear quadratic optimal solution under the following assumptions:                (i) the target has zero acceleration;        (ii) the object (a missile for example) has perfect response and complete control of its acceleration vector;        (iii) the object is launched on a near collision course, so that LOS angles are small; and        (iv) the object has zero acceleration along the LOS over all time.One or more of these assumptions, however, is not applicable in all situations.        
In order to remove assumption (i), an additional term may be added to the basic PN law that is equal to the target's estimated acceleration normal to the LOS multiplied by a proportionality gain. Thus, the so-called Augmented Proportional Navigation (APN) law was developed. In order to remove assumption (iv), the PN law was presented with respect to a new parameter: time-to-go.
Guidance laws based on optimal control and game theory approaches have been proposed in the literature. These guidance laws, however, have not been implemented in practice. Guidance laws developed using the optimal control and game theory approaches are generally able to more effectively counteract target maneuvers than the ordinary PN law; however, they assume that a maneuvering target's trajectory, as well as time-to-go and intercept point are known. In practice, such information is not known and can only be evaluated approximately. The prediction accuracy of these approximations influence significantly the intercept accuracy. Moreover, optimal guidance laws obtained for the first-order models of flight control systems and applied for the third-order models, which are closer to reality, may give even worse results than the PN law.
Guidance laws developed using the game and control theory approaches analyze and offer additional improvements over PN and APN by using additional information or improving the quality of existing guidance channel information, without changing the guidance law structure, i.e., they all belong to the class of PN guidance laws ( PRONAV). Prior to the present invention, PRONAV has continued to dominate research and development activity with respect to guidance laws. Because PRONAV implements parallel navigation, which is defined by the rule {dot over (λ)}(t)=0 for the planar LOS guidance (with an additional requirement {dot over (r)}(t)<0, where λ(t) is a LOS angle with respect to the reference axis and r(t) represents the target-to-missile range) or {dot over (λ)}s(t)=0, s=1,2,3, for the three-dimensional case (where λs(t) are LOS coordinates), a more general problem can be formulated to describe a class of improved guidance laws that will implement parallel navigation.
Prior known PN guidance laws (PRONAV), originated from proportional navigation which is based on an intuitive approach, give insufficient accuracy in many practical cases, especially for maneuvering targets. Thus, there remains a need for systems and methods that use improved guidance laws. In addition, there remains a need for systems and methods that improve upon the prior known PN guidance laws. Specifically, there remains a need for guidance laws that guarantee shorter time-t-go requirements and larger capture areas.